heat and mass transfer in a gypsum board subjected to fire - comsol … · 2011-12-01 ·...
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Willkommen Welcome Bienvenue
Heat and Mass Transfer in a Gypsum Board Subjected to Fire
Benedikt Weber Swiss Federal Laboratories for Material Science and Technology Dübendorf, Switzerland
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Gypsum boards are widely used in construction for partition walls Resistance to fire Heat barrier due to dehydration (chemical reaction)
Vapour release (pure gypsum 21%, actual board 17%) Endothermic reaction (consumes energy)
Motivation, dehydration
DSC: Differential scanning calorimetry TGA: Thermographic analysis
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Physical model
Porous medium Heat conduction Dehydration front
Heat sink Vapour source
Gaseous mixture of dry air and vapour Darcy’s law Fick’s law Paper liner
Condensation / evaporation (heat of phase change)
1-D behavior
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Main equations
Heat equation (porous media)
Conservation of gaseous mixture (Darcy)
Conservation of vapour (Concentrated Species)
g
g g
g
pv
v g eff vD j
dehyd evap(1 )
g g gS m mt
v
dehyd evap(1 ) · ( )(1 )
v
g vg vg vS m mt
v j
dehyd dehyd evap
eff
evap
·
p g pg g
pa a pv vC C
TC k T C T
t
H mT m H
v
j j
Change in weak form: Porosity
Modified source: Source from other phases (V4.2 in interface)
Modified source: Energy transport by interdiffusion
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Condensation and evaporation
Non-equilibrium formulation (penalty formulation)
Avoid evaporation for
Conservation of liquid water (immobile)
evap sat
w
v
Mm K p p
RT
0 min sat1 ( ) ( ) vK K H S S H p p
evap
wS mt
minS S
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Fire test
Temperature plateau
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Results without condensation – Pressure
Small gas pressure built-up Humidity less than 100% (partial vapor pressure < saturation press.) Paper liner prevents vapor from leaving the board Condensation expected 2 – 8 min (only indication)
Cold side with paper liner (low mass transfer)
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Vapor produced at dehydration front, mode in both directions Negligible air flux Vapor flux in quiescent air (diffusion dominated)
Results without condensation – Mass flux
Vapor Air
hot cold
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Vapor transport has no influence on temperature (compared to conduction)
Temperature plateau not captured
Results without condensation – Temperature at cold face
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Results with condensation – Saturation and evaporation
Water accumulated near cold face (saturation) Water pushed to cold face by successive evaporation and
condensation
Saturation Evaporation
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Results with condensation – Temperature
Temperature plateau well captured
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Conclusions
Gypsum board modeled as porous material Heat conduction Dehydration with heat sink and vapor source Mass transfer, mainly diffusion Condensation and evaporation produces temperature plateau
COMSOL very versatile
Derive differential equations Some adjustments needed in standard equations Relatively easy to try out various models
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Thank you for your attention!